MinT - Best Known (106−30, 106, s)-Nets in Base 2

Best Known (106−30, 106, s)-Nets in Base 2

(106−30, 106, 84)-Net over F₂ — Constructive and digital

Digital (76, 106, 84)-net over F₂, using

2¹ times duplication [i] based on digital (75, 105, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 35, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(106−30, 106, 124)-Net over F₂ — Digital

Digital (76, 106, 124)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−30, 106, 839)-Net in Base 2 — Upper bound on s

There is no (76, 106, 840)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 82 075349 148455 167223 666582 444408 > 2¹⁰⁶ [i]